American trio Jeff Overton, Jason Bohn and Blake Adams shared the first round lead in Fort Worth after seven under par rounds of 63.
A round of 64 saw Davis on his own just one shot further back as he looked to bounce back having failed to secure an Open Championship place at a qualifier earlier this week.
Of the leading trio, only Overton enjoyed a bogey-free opening round while Adams and Bohn suffered one apiece at the Colonial Country Club in Texas.
Davis just bogeyed the ninth and picked up seven birdies in an impressive six under round, while fellow Englishmen Paul Casey and Justin Rose were also in touch.
Casey was in a share of 14th after a four-under 66 while Rose was among a large group tied for 19th following a 67.
Davis' round was all the more impressive as he left to see a doctor about a horribly swollen face caused by an abscess in his mouth.
Meanwhile, 2008 winner Phil Mickelson endured a difficult day with a one over 71 to leave him in a share of 89th. Defending champion Steve Stricker fared better with a 68.